For a cylinder of density $1.5 g c m^{- 3}$ , buoyant force is $4 N$ inside a liquid of density d. Find the buoyant force for the same inside a liquid of density $3 d$

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Solution

Buoyancy force is equal to weight of liquid displaced and $ρ_{l i q u i d = d}$
$F = V ρ_{l i q u i d} g = V d g = 4 N$
now when the density become 3d
$F_{1} = V \times ρ_{n e w} g = V \times 3 d \times g = 3 F$
$F_{1} = 3 \times 4 = 12 N$

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Similar questions

Q. A cylinder made up of a material of density

1.5 g c m^{- 3}

is immersed inside a liquid of density

1 g c m^{- 3}

. State whether the cylinder moves up or not.

Q. A cylinder having cross sectional area

A

of density

ρ_{s}

is floating in two liquids as shown in figure inside a sealed container. (Assume atmospheric pressure as negligible). Liquid-1 has density

ρ_{1}

and liquid-2 has density

ρ_{2}

. Match the following for given two columns.

Column I Column II

i. Net force on cylinder from liquid-1	1. Zero
ii. Net force on cylinder from liquid-2	2. ( $ρ_{1} h_{2}$ + $ρ_{2} h_{3}$ ) $g A$
iii. Density of solid ( $ρ_{s}$ )	3. Net upthrust
iv. Buoyant Force	4. $ρ_{s} g A$ ( $h_{1}$ + $h_{2}$ + $h_{3}$ )
	5. $ρ_{1} g h_{2} A$
	6. $\frac{ρ_{1} h_{2} + ρ_{2} h_{3}}{h_{1} + h_{2} + h_{3}}$

Fill in the blank:

The buoyant force exerted by a liquid _______ with the decrease in density of liquid.

Write true or false for each statement:

(a) Equal volumes of the two different substances have equal masses.

(b) The density of a piece of brass will change by changing its size or shape.

(d) Relative density of water is 1.0.

(e) Relative density of a substance is expressed in g $c m^{-} 3$ .

(f) When a body is immersed in a liquid, the buoyant force experienced by the body is equal to the volume of the displaced by it.

(g) A body experiences the same buoyant force while floating in water or alcohol.

(h) A body experiences the same buoyant force when it floats or sinks in water.

(i) A body floats in a liquid when its weight becomes equal to the weight of the liquid displaced by its submerged part.

(j) A body while floating sinks in a liquid of low density than in high density.

A body of mass $10 k g$ and volume $0.5 m^{3}$ is placed in a liquid. What is the density of the liquid when buoyant force is equal to weight of the body? (Take acceleration due to gravity = $10 m / s^{2}$ )

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For a cylinder of density 1.5 g cm−3, buoyant force is 4 N inside a liquid of density d. Find the buoyant force for the same inside a liquid of density 3d

Buoyancy force is equal to weight of liquid displaced and ρliquid=dF=Vρliquidg=Vdg=4Nnow when the density become 3dF1=V×ρnewg=V×3d×g=3FF1=3×4=12N

For a cylinder of density $1.5 g c m^{- 3}$ , buoyant force is $4 N$ inside a liquid of density d. Find the buoyant force for the same inside a liquid of density $3 d$

Buoyancy force is equal to weight of liquid displaced and $ρ_{l i q u i d = d}$
$F = V ρ_{l i q u i d} g = V d g = 4 N$
now when the density become 3d
$F_{1} = V \times ρ_{n e w} g = V \times 3 d \times g = 3 F$
$F_{1} = 3 \times 4 = 12 N$